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14 Nov 2024, 01:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
64% (01:43) correct
36%
(01:42)
wrong
based on 132
sessions
History
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Time
Result
Not Attempted Yet
John went to the store and purchased a apples, b bananas and c cranberries. If the average number of pieces of each type of fruit purchased was 20 then how many apples were purchased?
(1) John purchased 30 fewer apples than bananas and cranberries combined.
(2) Total number of cranberries and bananas purchased was 15 fewer than the total number of pieces of fruit purchased.
(1) John purchased 30 fewer apples than bananas and cranberries combined.
(2) Total number of cranberries and bananas purchased was 15 fewer than the total number of pieces of fruit purchased.
14 Nov 2024, 04:07
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ANSWER IS D.
Since the average pieces of fruit of each type is 20, there must be a total of 60 pieces. 20*3
If the # of apples is x, Bananas (b) + Cranberries (c) must be 60-x.
From (1)
60-x-x=30
2x=30
x=15
SUFFICIENT
From (2)
60-x=60-15
x=15
SUFFICIENT
Since the average pieces of fruit of each type is 20, there must be a total of 60 pieces. 20*3
If the # of apples is x, Bananas (b) + Cranberries (c) must be 60-x.
From (1)
60-x-x=30
2x=30
x=15
SUFFICIENT
From (2)
60-x=60-15
x=15
SUFFICIENT
14 Nov 2024, 06:00
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IMO answer A is the correct one.
(a+b+c)/3=20
a+b+c=60
1. John purchased 30 fewer apples that bananas and cranberries combined.
This translates to: a=(b+c)-30
We also know from the given information: a+b+c=60
Substitute: a=(b+c)-30 into a+b+c=60
((b+c)-30)+b+c=60
b+c-30+b+c=60
2(b+c)=90
b+c=45
Now, substitute b+c=45 into a=(b+c)-30
a=45-30=15. Voila
2. The total number of cranberries and bananas purchased was 15 fewer than the total number of pieces of fruit purchased.
This translates to: b+c=(a+b+c)-15
Since a+b+c=60, we have, b+c=60-15; b+c=45
However, this only gives us the value of b+c and no direct information to solve for a alone. Without a relationship between a and b+c, we cannot determine the value of a.
So, Statement 2 alone is not sufficient.
In conclusion, only Statement 1 is sufficient to determine the number of apples purchased.
(a+b+c)/3=20
a+b+c=60
1. John purchased 30 fewer apples that bananas and cranberries combined.
This translates to: a=(b+c)-30
We also know from the given information: a+b+c=60
Substitute: a=(b+c)-30 into a+b+c=60
((b+c)-30)+b+c=60
b+c-30+b+c=60
2(b+c)=90
b+c=45
Now, substitute b+c=45 into a=(b+c)-30
a=45-30=15. Voila
2. The total number of cranberries and bananas purchased was 15 fewer than the total number of pieces of fruit purchased.
This translates to: b+c=(a+b+c)-15
Since a+b+c=60, we have, b+c=60-15; b+c=45
However, this only gives us the value of b+c and no direct information to solve for a alone. Without a relationship between a and b+c, we cannot determine the value of a.
So, Statement 2 alone is not sufficient.
In conclusion, only Statement 1 is sufficient to determine the number of apples purchased.
